1. Technical Field of the Invention
The present invention relates in general to the field of wall shear stress or skin friction measurement. The invention relates in particular to a new instrument for the accurate measurement of skin friction on a model or a body subjected to an air flow or a body subjected to a fluid flow. More specifically, the instrument of the present invention enables the determination over large regions of two-dimensional (2D) wall shear stress vectors acting on a surface which bounds a three-dimensional (3D) fluid flow.
2. Description of the Prior Art
Numerous commonly used devices such as aircraft, automobiles, pumps, turbines, etc., involve a three-dimensional fluid flow bounded by solid surfaces. The performance of these devices is predominately determined by the pressure normal stress and the wall shear stresses generated by the fluid flow, which act on the solid surfaces. As an example, lift and drag forces act on a commercial aircraft at transonic cruise conditions. The lift force counteracts gravity and allows the aircraft to fly, while the drag force must be countered by the propulsion system which consumes fuel.
The lift force is predominately generated by the wall pressure acting on the aircraft surfaces (e.g., wings, etc.) and the drag force is generated by a combination of the wall pressure and the wall shear stress acting on the aircraft surfaces(e.g., wings, tail and fuselage, etc.). Typically, about one-half of the drag of such a commercial aircraft at transonic cruise can be attributed directly to the wall shear stresses. Since considerable fuel is consumed to provide propulsion to overcome this drag force, it is clear that the wall shear stress has an important impact on the economics of the aircraft industry. Further, the extensive measurement of the wall shear stress can result in a better understanding of aerodynamic technology upon which aircraft designs are based.
The wall shear stress (.tau..sub.x (x,z) and .tau..sub.z (x,z)) is a vector which lies in the plane of the surface, and which may vary over the surface. The wall shear stress signifies a force per unit area applied to the surface by the flow of a fluid over that surface. In contrast, the wall pressure, P(x, z), is a scalar quantity which may vary over a surface, and signifies the force per unit area applied normal to the surface by the fluid immediately adjacent to the surface.
There exists a variety of techniques for measuring wall shear stress. Some of these conventional techniques include Preston tubes, surface fences, surface balances, surface hot films, log-law analysis of velocity profiles, liquid crystal (Reda, D. C., Muratore, J. J. Jr., Heineck, J. T., "Time and Flow-Direction Responses of Shear-Stress-Sensitive Liquid Crystal Coatings," AIAA Journal, vol. 32, no. 4, 1994, pp. 693-700) and oil film interferometry. For a more complete review of existing wall shear stress measurement techniques reference is made to Winter, K. G., "An Outline of the Techniques Available for the Measurement of Skin Friction in Turbulent Boundary Layers," Progress in Aeronautical Sciences, vol. 18, 1977, pp. 1-57; and Settles, G. S., "Recent Skin Friction Techniques for Compressible Flows," AIAA paper 86-1099, May, 1986.
Existing instruments include inherent limitations that prevent extensive use in a wind-tunnel or flight test environment. Most of these instruments, such as Preston tube, surface fence, surface balance, hot films and the log-law velocity profile analysis, allow for only a measurement at a single point on the surface. Further, the direction of the wall shear stress vector must be known, for instance from a surface oil-flow visualization where dots of oil are placed on the surface and are allowed to flow in the direction of the local wall shear stress.
The liquid crystal technique provides measurement of wall shear stress magnitude and direction but the theory behind this instrument is not rigorous and requires a complicated in-situ calibration process using another wall shear stress instrument.
Prior forms of the oil film interferometer wall shear stress instruments provided only measurements of wall shear stress at a point or along a line of oil, and the direction of the wall shear stress was needed either apriori or from another technique. Such limitations meant that wind-tunnel and flight test programs to develop aircraft designs do not benefit from extensive wall shear stress measurements. These measurements serve to improve lower drag designs.
Tanner, L. H. and Blows, L. G., "A Study of the Motion of Oil Films on Surfaces in Air Flow, with Application to the Measurement of Skin Friction", Journal of Physics E: Scientific Instrumentation, vol. 9, pp 194-202, 1976; Tanner, L. H., "A Skin Friction Meter, Using the Viscosity Balance Principle, Suitable for Use with Flat or Curved Metal Surfaces," Journal of Physics E: Scientific Instrumentation, vol. 10, pp 278-284, 1977; and Tanner, L. H., "A Comparison of the Viscosity Balance and Preston Tube Methods of Skin Friction Measurement," Journal of Physics E: Scientific Instrumentation, vol. 10, pp 627-632, 1977, describe the concept of the oil film interferometric measurement of wall shear stress. These articles present an instrument that measures the wall shear stress at a single point on a test surface. A thin straight line of oil is placed onto a test surface, approximately normal to the anticipated flow direction. The wind tunnel is started and air flows over the test surface. The oil flows in response to the wall shear stress imposed by the air flow. As a consequence of the oil flow, the oil film thickness decreases with time.
The thickness of the oil film at a single measurement point is determined optically using a low-power laser beam directed normal to the surface. Part of the incident light is reflected by the oil/air interface. Another portion of the incident light is reflected by the polished solid test surface. The two reflected light beams are imaged onto a photodetector. At the photodetector optical constructive/destructive interference between these two reflected beams occurs according to the difference in path length taken by each of the reflected beams. The time variation of the photodetector voltage output is recorded.
Constructive optical interference of the two optical reflections results in a local maximum in the photodetector voltage time history and occurs when the oil film has a thickness "h" that satisfies the following relation: EQU h=j.lambda./2n.sub.0,
where "j" is an integer equal to 0, 1, 2, . . . ; ".lambda." is the wavelength of the light in vacuum; and "n.sub.0 " is the oil index of refraction.
Destructive optical interference of the two optical reflections results in a local minimum in the photodetector voltage time history and occurs when the oil film has a thickness "h" defined as follows: EQU h=+1/2).lambda./2n.sub.0.
The thickness of the oil film is then deduced at discrete times when a local maximum or minimum occurs. Similarity analysis of the oil film flow may be made for an assumption of constant "X", resulting in the following similarity equation: EQU h=.mu.x/.tau.t,
where "x" is the distance from the oil line leading edge; "t" is the time from the start of the flow; ".mu." is the dynamic viscosity of the oil; and ".tau." is the shear stress component normal to the oil line leading edge.
The foregoing "Tanners and Blows" instrument has proven to be quite accurate, but is restricted to one measurement at a single point, and measures only the component of wall shear stress in the direction normal to the oil line leading edge.
Tanner, L. H. and Kulkarni, V. G., "The Viscosity Balance Method of Skin Friction Measurement: Further Developments including Applications to Three-Dimensional Flow," Journal of Physics E: Scientific Instruments, Vol 9, 1976, pp 1114-1121 presented an oil film interferometric method to measure the wall shear stress generated by a three-dimensional flow. This method analyzed the fringe pattern developed in individual drops of clear oil that were placed on the test surface. Analysis of a single interferogram image of the oil drop involved locating each discrete dark and light fringe, plotting the associated discrete heights (for each bright and dark fringe) along the drop centerline, and then analyzing by graphical integration along the drop centerline for the shear stress magnitude variation along the centerline of each drop according to the a generalization of the similarity relation: ##EQU1## where, .theta. is the "streamline" spacing or spacing between oil dots, t is total flow time, and s is the distance along the oil drop centerline. It should be noted that Tanner and Kulkarni nomenclature use n rather than .theta., y rather than h, etc.
Much of the analysis which Tanner and Kulkarni described relied on "fortuitous polynomial fits". Also used was their "similarity" assumption, even for 3D, that dh/dx was proportional to 1/.tau.. This method could result in the 3D shear stress vector but only for those discrete lines along which the oil drop would flow rather than continuously over the entire surface, used only the dark and bright fringes rather than each point (or camera pixel) of the entire image, made use of the approximation of the similarity relation rather than a more exact and rigorous treatment of the oil flow, and required a difficult and somewhat ambiguous determination of the surface streamline spacing.
Monson, in U.S. Pat. No. 4,377,343 introduce a dual-beam skin-friction interferometer which was a variant of the Tanners and Blow single-point instrument. The instrument provides for greater portability, ease-of-use, and alleviates the need to find the oil leading edge. However, only a single point measurement per wind tunnel run was measurable using the Monson instrument.
Bandyopadhyay et al. in U.S. Pat. No. 5,178,004 disclose a reflection type skin friction meter which relies upon measuring the slope of the oil-air interface rather than the thickness based on the similarity equation identified above. The Bandyopadhyay et al. skin friction meter uses a light beam and is basically a single point measurement system.
Monson, D. J., Mateer, G. G., and Menter, F. R., "Boundary-Layer Transition and Global Skin Friction Measurement with an Oil-Fringe Imaging Technique" SAE Paper No. 932550, September, 1993 describe an instrument referred to as the Fringe Imaging Skin Friction (FISF instrument). The FISF instrument relates to the holographic interferometric form of Tanner and Blow, but did not require a laser. A monochromatic light source was used instead of a laser, thus reducing safety requirements.
The FISF instrument provides measurement of the wall shear stress variation along the oil line. Only the component of the wall shear stress vector normal to the oil line leading edge is measured. The FISF instrument improvement over existing instruments resides in the ability to accomplish measurement for each point along the line during a single wind tunnel run, rather than taking measurement at a single point, thus considerably improving the efficiency of the instrument. However, the use of the similarity analysis for the derivation of the wall shear stress from oil film thickness reduces the accuracy of the results in particular for those regions of the surface where the direction of the wall shear stress varies.
Therefore, there is a significant and still unfulfilled need for a new oil film interferometer which addresses the foregoing limitations of existing instruments, and which enables a practical, simple, accurate, rapid measurement of the wall shear stress vector over large areas of an aerodynamic test surface.